Properties

Label 403.2.bt.a.82.12
Level $403$
Weight $2$
Character 403.82
Analytic conductor $3.218$
Analytic rank $0$
Dimension $280$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [403,2,Mod(82,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([5, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.bt (of order \(30\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(280\)
Relative dimension: \(35\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 82.12
Character \(\chi\) \(=\) 403.82
Dual form 403.2.bt.a.231.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.219621 + 1.03324i) q^{2} +(2.09766 - 0.445872i) q^{3} +(0.807749 + 0.359633i) q^{4} +(-3.00000 + 1.73205i) q^{5} +2.26530i q^{6} +(-0.0849215 - 0.116884i) q^{7} +(-1.79076 + 2.46477i) q^{8} +(1.46075 - 0.650366i) q^{9} +O(q^{10})\) \(q+(-0.219621 + 1.03324i) q^{2} +(2.09766 - 0.445872i) q^{3} +(0.807749 + 0.359633i) q^{4} +(-3.00000 + 1.73205i) q^{5} +2.26530i q^{6} +(-0.0849215 - 0.116884i) q^{7} +(-1.79076 + 2.46477i) q^{8} +(1.46075 - 0.650366i) q^{9} +(-1.13075 - 3.48010i) q^{10} +(1.07251 + 1.47618i) q^{11} +(1.85474 + 0.394236i) q^{12} +(1.10133 + 3.43323i) q^{13} +(0.139420 - 0.0620736i) q^{14} +(-5.52071 + 4.97087i) q^{15} +(-0.970120 - 1.07743i) q^{16} +(-1.35086 - 0.981457i) q^{17} +(0.351171 + 1.65213i) q^{18} +(-0.521127 + 0.169324i) q^{19} +(-3.04615 + 0.320163i) q^{20} +(-0.230252 - 0.207320i) q^{21} +(-1.76079 + 0.783954i) q^{22} +(6.67824 - 2.97334i) q^{23} +(-2.65744 + 5.96870i) q^{24} +(3.49999 - 6.06216i) q^{25} +(-3.78921 + 0.383919i) q^{26} +(-2.43070 + 1.76601i) q^{27} +(-0.0265598 - 0.124954i) q^{28} +(4.01836 + 0.854130i) q^{29} +(-3.92361 - 6.79590i) q^{30} +(3.75098 - 4.11462i) q^{31} +(-3.95061 + 2.28089i) q^{32} +(2.90795 + 2.61833i) q^{33} +(1.31075 - 1.18021i) q^{34} +(0.457214 + 0.203565i) q^{35} +1.41381 q^{36} +(9.71233 - 5.60742i) q^{37} +(-0.0605016 - 0.575634i) q^{38} +(3.84099 + 6.71071i) q^{39} +(1.10317 - 10.4960i) q^{40} +(-1.19636 + 0.388722i) q^{41} +(0.264778 - 0.192373i) q^{42} +(-1.73156 - 5.32918i) q^{43} +(0.335434 + 1.57809i) q^{44} +(-3.25577 + 4.48118i) q^{45} +(1.60548 + 7.55320i) q^{46} +(-5.37460 - 1.74631i) q^{47} +(-2.51538 - 1.82753i) q^{48} +(2.15667 - 6.63754i) q^{49} +(5.49497 + 4.94769i) q^{50} +(-3.27125 - 1.45645i) q^{51} +(-0.345109 + 3.16926i) q^{52} +(-1.36575 + 12.9943i) q^{53} +(-1.29087 - 2.89934i) q^{54} +(-5.77434 - 2.57090i) q^{55} +0.440167 q^{56} +(-1.01765 + 0.587541i) q^{57} +(-1.76503 + 3.96433i) q^{58} +(-9.02847 - 2.93353i) q^{59} +(-6.24704 + 2.02979i) q^{60} +(1.43720 + 2.48930i) q^{61} +(3.42758 + 4.77931i) q^{62} +(-0.200066 - 0.115508i) q^{63} +(-2.38510 - 7.34057i) q^{64} +(-9.25050 - 8.39214i) q^{65} +(-3.34400 + 2.42955i) q^{66} -0.744299i q^{67} +(-0.738192 - 1.27859i) q^{68} +(12.6830 - 9.21471i) q^{69} +(-0.310744 + 0.427702i) q^{70} +(-3.19790 - 7.18259i) q^{71} +(-1.01284 + 4.76505i) q^{72} +(0.342899 - 0.770164i) q^{73} +(3.66075 + 11.2666i) q^{74} +(4.63885 - 14.2769i) q^{75} +(-0.481835 - 0.0506429i) q^{76} +(0.0814636 - 0.250719i) q^{77} +(-7.77730 + 2.49483i) q^{78} +(-2.17556 + 0.968623i) q^{79} +(4.77651 + 1.55198i) q^{80} +(-7.52116 + 8.35310i) q^{81} +(-0.138895 - 1.32150i) q^{82} +(7.22534 + 6.50573i) q^{83} +(-0.111427 - 0.250269i) q^{84} +(5.75251 + 0.604613i) q^{85} +(5.88659 - 0.618705i) q^{86} +8.81000 q^{87} -5.55906 q^{88} +(12.3150 - 1.29436i) q^{89} +(-3.91508 - 4.34813i) q^{90} +(0.307765 - 0.420283i) q^{91} +6.46366 q^{92} +(6.03370 - 10.3035i) q^{93} +(2.98473 - 5.16970i) q^{94} +(1.27010 - 1.41059i) q^{95} +(-7.27007 + 6.54600i) q^{96} +(0.417981 - 0.938800i) q^{97} +(6.38449 + 3.68609i) q^{98} +(2.52672 + 1.45880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 280 q - 9 q^{2} - 3 q^{3} - 35 q^{4} - 15 q^{7} + 45 q^{8} + 24 q^{9} + 3 q^{10} - 8 q^{12} - 6 q^{13} + 4 q^{14} - 45 q^{15} + 23 q^{16} + 27 q^{17} + 45 q^{18} - 15 q^{19} - 12 q^{20} - 76 q^{21} + 41 q^{22} - 10 q^{23} - 33 q^{24} + 96 q^{25} + 9 q^{26} - 24 q^{27} - 32 q^{28} + 13 q^{29} + 36 q^{30} + 2 q^{31} - 141 q^{32} - 93 q^{33} - 9 q^{34} - 43 q^{35} - 194 q^{36} + 3 q^{37} - 49 q^{38} + 50 q^{39} - 75 q^{40} - 15 q^{41} + 17 q^{42} + 33 q^{43} + 18 q^{44} - 15 q^{45} - 9 q^{46} - 59 q^{48} + 3 q^{49} + 36 q^{50} + 47 q^{51} - 56 q^{52} + 12 q^{53} - 33 q^{54} - 5 q^{55} - 50 q^{56} - 105 q^{57} - 3 q^{58} - 15 q^{59} + 90 q^{60} - 57 q^{61} - 72 q^{62} + 201 q^{63} + 13 q^{64} - 43 q^{65} + 22 q^{66} - 71 q^{68} - 7 q^{69} - 42 q^{71} + 90 q^{72} + 9 q^{73} - 113 q^{74} + 45 q^{75} + 14 q^{76} - 24 q^{77} + 61 q^{78} + 54 q^{79} + 30 q^{80} + 106 q^{81} + 16 q^{82} + 54 q^{83} + 60 q^{84} + 18 q^{85} + 84 q^{86} + 42 q^{87} - 98 q^{88} - 99 q^{89} + 11 q^{90} + 60 q^{91} + 266 q^{92} - 104 q^{93} + 33 q^{94} - 120 q^{95} + 204 q^{96} - 50 q^{97} - 15 q^{98} - 168 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{15}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.219621 + 1.03324i −0.155295 + 0.730608i 0.829725 + 0.558172i \(0.188497\pi\)
−0.985021 + 0.172436i \(0.944836\pi\)
\(3\) 2.09766 0.445872i 1.21109 0.257424i 0.442262 0.896886i \(-0.354176\pi\)
0.768823 + 0.639462i \(0.220843\pi\)
\(4\) 0.807749 + 0.359633i 0.403875 + 0.179817i
\(5\) −3.00000 + 1.73205i −1.34164 + 0.774596i −0.987048 0.160425i \(-0.948713\pi\)
−0.354592 + 0.935021i \(0.615380\pi\)
\(6\) 2.26530i 0.924805i
\(7\) −0.0849215 0.116884i −0.0320973 0.0441781i 0.792667 0.609655i \(-0.208692\pi\)
−0.824764 + 0.565477i \(0.808692\pi\)
\(8\) −1.79076 + 2.46477i −0.633130 + 0.871428i
\(9\) 1.46075 0.650366i 0.486915 0.216789i
\(10\) −1.13075 3.48010i −0.357575 1.10050i
\(11\) 1.07251 + 1.47618i 0.323374 + 0.445086i 0.939493 0.342567i \(-0.111296\pi\)
−0.616120 + 0.787652i \(0.711296\pi\)
\(12\) 1.85474 + 0.394236i 0.535416 + 0.113806i
\(13\) 1.10133 + 3.43323i 0.305453 + 0.952207i
\(14\) 0.139420 0.0620736i 0.0372614 0.0165899i
\(15\) −5.52071 + 4.97087i −1.42544 + 1.28347i
\(16\) −0.970120 1.07743i −0.242530 0.269357i
\(17\) −1.35086 0.981457i −0.327632 0.238038i 0.411793 0.911277i \(-0.364903\pi\)
−0.739425 + 0.673239i \(0.764903\pi\)
\(18\) 0.351171 + 1.65213i 0.0827717 + 0.389410i
\(19\) −0.521127 + 0.169324i −0.119555 + 0.0388457i −0.368183 0.929753i \(-0.620020\pi\)
0.248629 + 0.968599i \(0.420020\pi\)
\(20\) −3.04615 + 0.320163i −0.681140 + 0.0715907i
\(21\) −0.230252 0.207320i −0.0502451 0.0452409i
\(22\) −1.76079 + 0.783954i −0.375401 + 0.167139i
\(23\) 6.67824 2.97334i 1.39251 0.619985i 0.432931 0.901427i \(-0.357479\pi\)
0.959578 + 0.281442i \(0.0908128\pi\)
\(24\) −2.65744 + 5.96870i −0.542447 + 1.21836i
\(25\) 3.49999 6.06216i 0.699998 1.21243i
\(26\) −3.78921 + 0.383919i −0.743125 + 0.0752927i
\(27\) −2.43070 + 1.76601i −0.467788 + 0.339868i
\(28\) −0.0265598 0.124954i −0.00501932 0.0236141i
\(29\) 4.01836 + 0.854130i 0.746192 + 0.158608i 0.565289 0.824893i \(-0.308765\pi\)
0.180903 + 0.983501i \(0.442098\pi\)
\(30\) −3.92361 6.79590i −0.716350 1.24076i
\(31\) 3.75098 4.11462i 0.673697 0.739008i
\(32\) −3.95061 + 2.28089i −0.698377 + 0.403208i
\(33\) 2.90795 + 2.61833i 0.506209 + 0.455793i
\(34\) 1.31075 1.18021i 0.224792 0.202404i
\(35\) 0.457214 + 0.203565i 0.0772832 + 0.0344087i
\(36\) 1.41381 0.235635
\(37\) 9.71233 5.60742i 1.59670 0.921854i 0.604579 0.796545i \(-0.293341\pi\)
0.992118 0.125309i \(-0.0399921\pi\)
\(38\) −0.0605016 0.575634i −0.00981465 0.0933801i
\(39\) 3.84099 + 6.71071i 0.615051 + 1.07457i
\(40\) 1.10317 10.4960i 0.174427 1.65956i
\(41\) −1.19636 + 0.388722i −0.186841 + 0.0607082i −0.400943 0.916103i \(-0.631317\pi\)
0.214102 + 0.976811i \(0.431317\pi\)
\(42\) 0.264778 0.192373i 0.0408562 0.0296837i
\(43\) −1.73156 5.32918i −0.264060 0.812693i −0.991908 0.126955i \(-0.959480\pi\)
0.727849 0.685738i \(-0.240520\pi\)
\(44\) 0.335434 + 1.57809i 0.0505686 + 0.237907i
\(45\) −3.25577 + 4.48118i −0.485341 + 0.668015i
\(46\) 1.60548 + 7.55320i 0.236715 + 1.11366i
\(47\) −5.37460 1.74631i −0.783967 0.254726i −0.110434 0.993883i \(-0.535224\pi\)
−0.673533 + 0.739157i \(0.735224\pi\)
\(48\) −2.51538 1.82753i −0.363063 0.263781i
\(49\) 2.15667 6.63754i 0.308096 0.948221i
\(50\) 5.49497 + 4.94769i 0.777106 + 0.699709i
\(51\) −3.27125 1.45645i −0.458067 0.203944i
\(52\) −0.345109 + 3.16926i −0.0478580 + 0.439498i
\(53\) −1.36575 + 12.9943i −0.187601 + 1.78490i 0.345069 + 0.938577i \(0.387856\pi\)
−0.532670 + 0.846323i \(0.678811\pi\)
\(54\) −1.29087 2.89934i −0.175665 0.394550i
\(55\) −5.77434 2.57090i −0.778612 0.346661i
\(56\) 0.440167 0.0588198
\(57\) −1.01765 + 0.587541i −0.134791 + 0.0778217i
\(58\) −1.76503 + 3.96433i −0.231760 + 0.520542i
\(59\) −9.02847 2.93353i −1.17541 0.381913i −0.344748 0.938695i \(-0.612036\pi\)
−0.830659 + 0.556782i \(0.812036\pi\)
\(60\) −6.24704 + 2.02979i −0.806489 + 0.262044i
\(61\) 1.43720 + 2.48930i 0.184014 + 0.318722i 0.943244 0.332101i \(-0.107757\pi\)
−0.759230 + 0.650823i \(0.774424\pi\)
\(62\) 3.42758 + 4.77931i 0.435303 + 0.606973i
\(63\) −0.200066 0.115508i −0.0252060 0.0145527i
\(64\) −2.38510 7.34057i −0.298137 0.917571i
\(65\) −9.25050 8.39214i −1.14738 1.04092i
\(66\) −3.34400 + 2.42955i −0.411617 + 0.299058i
\(67\) 0.744299i 0.0909306i −0.998966 0.0454653i \(-0.985523\pi\)
0.998966 0.0454653i \(-0.0144770\pi\)
\(68\) −0.738192 1.27859i −0.0895189 0.155051i
\(69\) 12.6830 9.21471i 1.52685 1.10932i
\(70\) −0.310744 + 0.427702i −0.0371410 + 0.0511202i
\(71\) −3.19790 7.18259i −0.379520 0.852417i −0.997790 0.0664505i \(-0.978833\pi\)
0.618269 0.785966i \(-0.287834\pi\)
\(72\) −1.01284 + 4.76505i −0.119365 + 0.561567i
\(73\) 0.342899 0.770164i 0.0401333 0.0901409i −0.892366 0.451312i \(-0.850956\pi\)
0.932500 + 0.361171i \(0.117623\pi\)
\(74\) 3.66075 + 11.2666i 0.425553 + 1.30972i
\(75\) 4.63885 14.2769i 0.535648 1.64856i
\(76\) −0.481835 0.0506429i −0.0552702 0.00580913i
\(77\) 0.0814636 0.250719i 0.00928363 0.0285721i
\(78\) −7.77730 + 2.49483i −0.880606 + 0.282484i
\(79\) −2.17556 + 0.968623i −0.244770 + 0.108979i −0.525455 0.850821i \(-0.676105\pi\)
0.280685 + 0.959800i \(0.409438\pi\)
\(80\) 4.77651 + 1.55198i 0.534030 + 0.173517i
\(81\) −7.52116 + 8.35310i −0.835685 + 0.928122i
\(82\) −0.138895 1.32150i −0.0153384 0.145935i
\(83\) 7.22534 + 6.50573i 0.793084 + 0.714096i 0.962451 0.271457i \(-0.0875054\pi\)
−0.169366 + 0.985553i \(0.554172\pi\)
\(84\) −0.111427 0.250269i −0.0121577 0.0273066i
\(85\) 5.75251 + 0.604613i 0.623947 + 0.0655795i
\(86\) 5.88659 0.618705i 0.634767 0.0667167i
\(87\) 8.81000 0.944531
\(88\) −5.55906 −0.592597
\(89\) 12.3150 1.29436i 1.30539 0.137202i 0.573829 0.818975i \(-0.305458\pi\)
0.731564 + 0.681773i \(0.238791\pi\)
\(90\) −3.91508 4.34813i −0.412685 0.458334i
\(91\) 0.307765 0.420283i 0.0322625 0.0440576i
\(92\) 6.46366 0.673883
\(93\) 6.03370 10.3035i 0.625666 1.06843i
\(94\) 2.98473 5.16970i 0.307851 0.533214i
\(95\) 1.27010 1.41059i 0.130310 0.144724i
\(96\) −7.27007 + 6.54600i −0.741998 + 0.668098i
\(97\) 0.417981 0.938800i 0.0424395 0.0953207i −0.891082 0.453843i \(-0.850053\pi\)
0.933521 + 0.358522i \(0.116719\pi\)
\(98\) 6.38449 + 3.68609i 0.644931 + 0.372351i
\(99\) 2.52672 + 1.45880i 0.253945 + 0.146615i
\(100\) 5.00727 3.63800i 0.500727 0.363800i
\(101\) 2.04642 0.911127i 0.203627 0.0906605i −0.302389 0.953185i \(-0.597784\pi\)
0.506016 + 0.862524i \(0.331118\pi\)
\(102\) 2.22330 3.06010i 0.220139 0.302995i
\(103\) −6.49690 + 7.21554i −0.640159 + 0.710969i −0.972686 0.232125i \(-0.925432\pi\)
0.332527 + 0.943094i \(0.392099\pi\)
\(104\) −10.4343 3.43358i −1.02317 0.336690i
\(105\) 1.04984 + 0.223151i 0.102454 + 0.0217773i
\(106\) −13.1262 4.26496i −1.27493 0.414249i
\(107\) 0.903496 8.59619i 0.0873442 0.831025i −0.859889 0.510481i \(-0.829468\pi\)
0.947234 0.320544i \(-0.103866\pi\)
\(108\) −2.59851 + 0.552331i −0.250042 + 0.0531480i
\(109\) 16.5629 + 5.38160i 1.58643 + 0.515464i 0.963704 0.266973i \(-0.0860235\pi\)
0.622730 + 0.782437i \(0.286024\pi\)
\(110\) 3.92452 5.40163i 0.374188 0.515025i
\(111\) 17.8730 16.0929i 1.69643 1.52747i
\(112\) −0.0435504 + 0.204889i −0.00411513 + 0.0193601i
\(113\) −0.692488 6.58859i −0.0651438 0.619802i −0.977577 0.210577i \(-0.932466\pi\)
0.912433 0.409225i \(-0.134201\pi\)
\(114\) −0.383571 1.18051i −0.0359247 0.110565i
\(115\) −14.8847 + 20.4871i −1.38801 + 1.91043i
\(116\) 2.93866 + 2.13506i 0.272848 + 0.198235i
\(117\) 3.84161 + 4.29881i 0.355157 + 0.397426i
\(118\) 5.01387 8.68427i 0.461564 0.799452i
\(119\) 0.241241i 0.0221145i
\(120\) −2.36578 22.5089i −0.215965 2.05477i
\(121\) 2.37035 7.29519i 0.215486 0.663199i
\(122\) −2.88767 + 0.938261i −0.261437 + 0.0849461i
\(123\) −2.33624 + 1.34883i −0.210652 + 0.121620i
\(124\) 4.50961 1.97460i 0.404975 0.177325i
\(125\) 6.92814i 0.619671i
\(126\) 0.163286 0.181347i 0.0145467 0.0161557i
\(127\) 7.24409 1.53978i 0.642809 0.136633i 0.125037 0.992152i \(-0.460095\pi\)
0.517772 + 0.855519i \(0.326762\pi\)
\(128\) −0.965224 + 0.101449i −0.0853145 + 0.00896692i
\(129\) −6.00835 10.4068i −0.529006 0.916265i
\(130\) 10.7027 7.71486i 0.938685 0.676638i
\(131\) −0.570099 5.42413i −0.0498098 0.473909i −0.990786 0.135436i \(-0.956756\pi\)
0.940976 0.338473i \(-0.109910\pi\)
\(132\) 1.40726 + 3.16075i 0.122486 + 0.275108i
\(133\) 0.0640462 + 0.0465323i 0.00555351 + 0.00403486i
\(134\) 0.769036 + 0.163464i 0.0664346 + 0.0141211i
\(135\) 4.23328 9.50811i 0.364343 0.818328i
\(136\) 4.83813 1.57201i 0.414867 0.134798i
\(137\) 3.92213 3.53150i 0.335090 0.301717i −0.484358 0.874870i \(-0.660947\pi\)
0.819448 + 0.573153i \(0.194280\pi\)
\(138\) 6.73552 + 15.1282i 0.573365 + 1.28780i
\(139\) −19.1831 + 4.07748i −1.62709 + 0.345848i −0.928975 0.370143i \(-0.879309\pi\)
−0.698110 + 0.715990i \(0.745975\pi\)
\(140\) 0.296106 + 0.328858i 0.0250255 + 0.0277936i
\(141\) −12.0527 1.26679i −1.01502 0.106683i
\(142\) 8.12363 1.72673i 0.681720 0.144904i
\(143\) −3.88689 + 5.30793i −0.325038 + 0.443871i
\(144\) −2.11782 0.942914i −0.176485 0.0785762i
\(145\) −13.5345 + 4.39762i −1.12398 + 0.365202i
\(146\) 0.720453 + 0.523440i 0.0596251 + 0.0433202i
\(147\) 1.56447 14.8849i 0.129035 1.22769i
\(148\) 9.86174 1.03651i 0.810630 0.0852007i
\(149\) 7.60897i 0.623351i 0.950189 + 0.311676i \(0.100890\pi\)
−0.950189 + 0.311676i \(0.899110\pi\)
\(150\) 13.7326 + 7.92853i 1.12126 + 0.647362i
\(151\) −4.56532 6.28363i −0.371521 0.511355i 0.581793 0.813337i \(-0.302352\pi\)
−0.953313 + 0.301983i \(0.902352\pi\)
\(152\) 0.515868 1.58768i 0.0418424 0.128778i
\(153\) −2.61157 0.555106i −0.211133 0.0448777i
\(154\) 0.241161 + 0.139234i 0.0194333 + 0.0112198i
\(155\) −4.12622 + 18.8407i −0.331426 + 1.51333i
\(156\) 0.689164 + 6.80192i 0.0551773 + 0.544589i
\(157\) 4.44851 + 13.6911i 0.355030 + 1.09267i 0.955992 + 0.293392i \(0.0947841\pi\)
−0.600962 + 0.799277i \(0.705216\pi\)
\(158\) −0.523016 2.46060i −0.0416089 0.195755i
\(159\) 2.92889 + 27.8665i 0.232276 + 2.20996i
\(160\) 7.90122 13.6853i 0.624646 1.08192i
\(161\) −0.914663 0.528081i −0.0720856 0.0416186i
\(162\) −6.97891 9.60564i −0.548315 0.754691i
\(163\) −0.844047 0.0887130i −0.0661109 0.00694853i 0.0714153 0.997447i \(-0.477248\pi\)
−0.137526 + 0.990498i \(0.543915\pi\)
\(164\) −1.10616 0.116262i −0.0863765 0.00907854i
\(165\) −13.2589 2.81827i −1.03221 0.219402i
\(166\) −8.30878 + 6.03668i −0.644887 + 0.468538i
\(167\) 4.38505 + 3.94832i 0.339326 + 0.305530i 0.821122 0.570753i \(-0.193349\pi\)
−0.481796 + 0.876283i \(0.660015\pi\)
\(168\) 0.923322 0.196258i 0.0712358 0.0151416i
\(169\) −10.5742 + 7.56221i −0.813397 + 0.581709i
\(170\) −1.88808 + 5.81091i −0.144809 + 0.445676i
\(171\) −0.651111 + 0.586263i −0.0497917 + 0.0448327i
\(172\) 0.517888 4.92737i 0.0394886 0.375708i
\(173\) 9.45214 + 10.4977i 0.718633 + 0.798123i 0.986225 0.165409i \(-0.0528946\pi\)
−0.267592 + 0.963532i \(0.586228\pi\)
\(174\) −1.93486 + 9.10280i −0.146681 + 0.690082i
\(175\) −1.00580 + 0.105713i −0.0760311 + 0.00799119i
\(176\) 0.550016 2.58762i 0.0414590 0.195049i
\(177\) −20.2467 2.12801i −1.52183 0.159951i
\(178\) −1.36726 + 13.0086i −0.102480 + 0.975036i
\(179\) −22.0169 9.80256i −1.64562 0.732678i −0.646089 0.763262i \(-0.723597\pi\)
−0.999532 + 0.0305839i \(0.990263\pi\)
\(180\) −4.24143 + 2.44879i −0.316137 + 0.182522i
\(181\) −4.48679 7.77135i −0.333501 0.577640i 0.649695 0.760195i \(-0.274897\pi\)
−0.983196 + 0.182555i \(0.941563\pi\)
\(182\) 0.366659 + 0.410296i 0.0271786 + 0.0304132i
\(183\) 4.12466 + 4.58090i 0.304904 + 0.338630i
\(184\) −4.63052 + 21.7849i −0.341366 + 1.60600i
\(185\) −19.4246 + 33.6445i −1.42813 + 2.47359i
\(186\) 9.32085 + 8.49711i 0.683438 + 0.623038i
\(187\) 3.04674i 0.222799i
\(188\) −3.71330 3.34347i −0.270820 0.243848i
\(189\) 0.412837 + 0.134139i 0.0300295 + 0.00975717i
\(190\) 1.17853 + 1.62211i 0.0854996 + 0.117680i
\(191\) 5.99373 10.3815i 0.433691 0.751175i −0.563497 0.826118i \(-0.690544\pi\)
0.997188 + 0.0749431i \(0.0238775\pi\)
\(192\) −8.27607 14.3346i −0.597274 1.03451i
\(193\) −3.72271 + 8.36134i −0.267966 + 0.601862i −0.996541 0.0831044i \(-0.973517\pi\)
0.728575 + 0.684967i \(0.240183\pi\)
\(194\) 0.878204 + 0.638053i 0.0630514 + 0.0458095i
\(195\) −23.1462 13.4793i −1.65754 0.965275i
\(196\) 4.12913 4.58586i 0.294938 0.327562i
\(197\) −12.8128 17.6353i −0.912872 1.25646i −0.966176 0.257882i \(-0.916975\pi\)
0.0533041 0.998578i \(-0.483025\pi\)
\(198\) −2.06221 + 2.29031i −0.146555 + 0.162765i
\(199\) 13.2117 + 14.6731i 0.936552 + 1.04015i 0.999113 + 0.0421051i \(0.0134064\pi\)
−0.0625613 + 0.998041i \(0.519927\pi\)
\(200\) 8.67419 + 19.4826i 0.613358 + 1.37763i
\(201\) −0.331862 1.56129i −0.0234077 0.110125i
\(202\) 0.491971 + 2.31454i 0.0346149 + 0.162850i
\(203\) −0.241411 0.542218i −0.0169437 0.0380562i
\(204\) −2.11856 2.35290i −0.148329 0.164736i
\(205\) 2.91580 3.23833i 0.203648 0.226174i
\(206\) −6.02850 8.29751i −0.420025 0.578115i
\(207\) 7.82145 8.68660i 0.543628 0.603760i
\(208\) 2.63064 4.51724i 0.182402 0.313215i
\(209\) −0.808867 0.587676i −0.0559505 0.0406504i
\(210\) −0.461135 + 1.03573i −0.0318213 + 0.0714719i
\(211\) 9.23150 + 15.9894i 0.635523 + 1.10076i 0.986404 + 0.164338i \(0.0525487\pi\)
−0.350881 + 0.936420i \(0.614118\pi\)
\(212\) −5.77636 + 10.0049i −0.396722 + 0.687143i
\(213\) −9.91062 13.6408i −0.679064 0.934652i
\(214\) 8.68346 + 2.82143i 0.593589 + 0.192869i
\(215\) 14.4251 + 12.9884i 0.983782 + 0.885801i
\(216\) 9.15361i 0.622825i
\(217\) −0.799474 0.0890118i −0.0542718 0.00604251i
\(218\) −9.19801 + 15.9314i −0.622968 + 1.07901i
\(219\) 0.375892 1.76843i 0.0254004 0.119500i
\(220\) −3.73964 4.15329i −0.252127 0.280015i
\(221\) 1.88183 5.71872i 0.126586 0.384683i
\(222\) 12.7025 + 22.0013i 0.852535 + 1.47663i
\(223\) −13.9898 + 8.07701i −0.936826 + 0.540876i −0.888964 0.457977i \(-0.848574\pi\)
−0.0478618 + 0.998854i \(0.515241\pi\)
\(224\) 0.602092 + 0.268069i 0.0402290 + 0.0179111i
\(225\) 1.16997 11.1316i 0.0779982 0.742104i
\(226\) 6.95965 + 0.731488i 0.462949 + 0.0486579i
\(227\) 3.51363 16.5303i 0.233208 1.09716i −0.693233 0.720714i \(-0.743814\pi\)
0.926440 0.376441i \(-0.122852\pi\)
\(228\) −1.03331 + 0.108605i −0.0684324 + 0.00719253i
\(229\) −2.68757 + 12.6440i −0.177600 + 0.835542i 0.795644 + 0.605765i \(0.207133\pi\)
−0.973243 + 0.229776i \(0.926200\pi\)
\(230\) −17.8990 19.8788i −1.18022 1.31077i
\(231\) 0.0590944 0.562246i 0.00388813 0.0369931i
\(232\) −9.30116 + 8.37481i −0.610651 + 0.549833i
\(233\) −3.49808 + 10.7660i −0.229167 + 0.705303i 0.768675 + 0.639640i \(0.220916\pi\)
−0.997842 + 0.0656635i \(0.979084\pi\)
\(234\) −5.28538 + 3.02518i −0.345516 + 0.197762i
\(235\) 19.1485 4.07014i 1.24911 0.265507i
\(236\) −6.23775 5.61649i −0.406043 0.365603i
\(237\) −4.13171 + 3.00187i −0.268384 + 0.194992i
\(238\) −0.249259 0.0529816i −0.0161571 0.00343429i
\(239\) 16.4981 + 1.73402i 1.06717 + 0.112164i 0.621796 0.783179i \(-0.286403\pi\)
0.445376 + 0.895343i \(0.353070\pi\)
\(240\) 10.7115 + 1.12582i 0.691424 + 0.0726716i
\(241\) −10.3502 14.2458i −0.666716 0.917655i 0.332965 0.942939i \(-0.391951\pi\)
−0.999680 + 0.0252839i \(0.991951\pi\)
\(242\) 7.01706 + 4.05130i 0.451074 + 0.260428i
\(243\) −7.54568 + 13.0695i −0.484056 + 0.838409i
\(244\) 0.265661 + 2.52759i 0.0170072 + 0.161813i
\(245\) 5.02655 + 23.6481i 0.321135 + 1.51082i
\(246\) −0.880572 2.71012i −0.0561432 0.172791i
\(247\) −1.15526 1.60267i −0.0735075 0.101975i
\(248\) 3.42448 + 16.6136i 0.217455 + 1.05497i
\(249\) 18.0570 + 10.4252i 1.14432 + 0.660673i
\(250\) −7.15839 1.52156i −0.452737 0.0962321i
\(251\) 3.91676 12.0545i 0.247224 0.760876i −0.748039 0.663655i \(-0.769004\pi\)
0.995263 0.0972215i \(-0.0309955\pi\)
\(252\) −0.120063 0.165252i −0.00756325 0.0104099i
\(253\) 11.5517 + 6.66936i 0.726247 + 0.419299i
\(254\) 7.82301i 0.490859i
\(255\) 12.3364 1.29661i 0.772535 0.0811967i
\(256\) 1.72073 16.3717i 0.107546 1.02323i
\(257\) −18.6253 13.5321i −1.16181 0.844107i −0.171807 0.985131i \(-0.554961\pi\)
−0.990006 + 0.141024i \(0.954961\pi\)
\(258\) 12.0722 3.92250i 0.751582 0.244204i
\(259\) −1.48020 0.659030i −0.0919754 0.0409501i
\(260\) −4.45400 10.1055i −0.276225 0.626719i
\(261\) 6.42531 1.36574i 0.397716 0.0845372i
\(262\) 5.72961 + 0.602206i 0.353976 + 0.0372044i
\(263\) 3.19522 + 3.54866i 0.197026 + 0.218820i 0.833560 0.552429i \(-0.186299\pi\)
−0.636534 + 0.771249i \(0.719632\pi\)
\(264\) −11.6610 + 2.47863i −0.717686 + 0.152549i
\(265\) −18.4095 41.3483i −1.13088 2.54001i
\(266\) −0.0621447 + 0.0559554i −0.00381034 + 0.00343084i
\(267\) 25.2557 8.20607i 1.54562 0.502203i
\(268\) 0.267675 0.601207i 0.0163508 0.0367246i
\(269\) 17.7047 + 3.76326i 1.07948 + 0.229450i 0.713132 0.701030i \(-0.247276\pi\)
0.366344 + 0.930479i \(0.380609\pi\)
\(270\) 8.89439 + 6.46216i 0.541296 + 0.393274i
\(271\) −6.00251 13.4818i −0.364626 0.818964i −0.998946 0.0458934i \(-0.985387\pi\)
0.634320 0.773070i \(-0.281280\pi\)
\(272\) 0.253047 + 2.40758i 0.0153432 + 0.145981i
\(273\) 0.458194 1.01883i 0.0277312 0.0616627i
\(274\) 2.78749 + 4.82807i 0.168398 + 0.291675i
\(275\) 12.7026 1.33510i 0.765997 0.0805096i
\(276\) 13.5586 2.88196i 0.816130 0.173474i
\(277\) −15.2597 + 16.9476i −0.916868 + 1.01829i 0.0828955 + 0.996558i \(0.473583\pi\)
−0.999764 + 0.0217273i \(0.993083\pi\)
\(278\) 20.7161i 1.24247i
\(279\) 2.80323 8.44993i 0.167825 0.505884i
\(280\) −1.32050 + 0.762391i −0.0789150 + 0.0455616i
\(281\) −25.7485 + 8.36618i −1.53602 + 0.499085i −0.950276 0.311408i \(-0.899199\pi\)
−0.585748 + 0.810493i \(0.699199\pi\)
\(282\) 3.95593 12.1751i 0.235572 0.725016i
\(283\) −0.0591920 0.563174i −0.00351860 0.0334772i 0.992622 0.121252i \(-0.0386910\pi\)
−0.996140 + 0.0877751i \(0.972024\pi\)
\(284\) 6.95180i 0.412514i
\(285\) 2.03530 3.52524i 0.120561 0.208817i
\(286\) −4.63070 5.18181i −0.273819 0.306407i
\(287\) 0.147032 + 0.106825i 0.00867905 + 0.00630570i
\(288\) −4.28743 + 5.90114i −0.252639 + 0.347728i
\(289\) −4.39172 13.5163i −0.258337 0.795079i
\(290\) −1.57132 14.9501i −0.0922711 0.877901i
\(291\) 0.458198 2.15565i 0.0268600 0.126366i
\(292\) 0.553953 0.498782i 0.0324177 0.0291890i
\(293\) −8.23062 + 11.3285i −0.480838 + 0.661816i −0.978666 0.205460i \(-0.934131\pi\)
0.497828 + 0.867276i \(0.334131\pi\)
\(294\) 15.0360 + 4.88550i 0.876919 + 0.284928i
\(295\) 32.1664 6.83718i 1.87280 0.398076i
\(296\) −3.57146 + 33.9802i −0.207587 + 1.97506i
\(297\) −5.21389 1.69410i −0.302541 0.0983015i
\(298\) −7.86186 1.67109i −0.455425 0.0968036i
\(299\) 17.5631 + 19.6533i 1.01570 + 1.13658i
\(300\) 8.88148 9.86388i 0.512773 0.569492i
\(301\) −0.475852 + 0.654954i −0.0274277 + 0.0377509i
\(302\) 7.49511 3.33704i 0.431295 0.192025i
\(303\) 3.88646 2.82368i 0.223271 0.162216i
\(304\) 0.687990 + 0.397211i 0.0394589 + 0.0227816i
\(305\) −8.62318 4.97859i −0.493762 0.285073i
\(306\) 1.14711 2.57645i 0.0655759 0.147286i
\(307\) −16.5026 + 14.8590i −0.941851 + 0.848046i −0.988555 0.150863i \(-0.951795\pi\)
0.0467042 + 0.998909i \(0.485128\pi\)
\(308\) 0.155969 0.173221i 0.00888716 0.00987019i
\(309\) −10.4111 + 18.0326i −0.592267 + 1.02584i
\(310\) −18.5607 8.40118i −1.05418 0.477155i
\(311\) 3.36010 0.190534 0.0952669 0.995452i \(-0.469630\pi\)
0.0952669 + 0.995452i \(0.469630\pi\)
\(312\) −23.4187 2.55011i −1.32582 0.144372i
\(313\) 6.48923 + 7.20702i 0.366793 + 0.407365i 0.898084 0.439825i \(-0.144959\pi\)
−0.531291 + 0.847190i \(0.678293\pi\)
\(314\) −15.1231 + 1.58950i −0.853447 + 0.0897009i
\(315\) 0.800265 0.0450898
\(316\) −2.10566 −0.118453
\(317\) −14.4921 + 1.52319i −0.813960 + 0.0855506i −0.502355 0.864661i \(-0.667533\pi\)
−0.311604 + 0.950212i \(0.600866\pi\)
\(318\) −29.4359 3.09384i −1.65068 0.173494i
\(319\) 3.04888 + 6.84790i 0.170705 + 0.383409i
\(320\) 19.8695 + 17.8906i 1.11074 + 1.00011i
\(321\) −1.93757 18.4347i −0.108145 1.02893i
\(322\) 0.746511 0.829085i 0.0416014 0.0462031i
\(323\) 0.870154 + 0.282730i 0.0484167 + 0.0157315i
\(324\) −9.07927 + 4.04235i −0.504404 + 0.224575i
\(325\) 24.6674 + 5.33986i 1.36830 + 0.296202i
\(326\) 0.277032 0.852616i 0.0153434 0.0472220i
\(327\) 37.1428 + 3.90386i 2.05400 + 0.215884i
\(328\) 1.18429 3.64487i 0.0653915 0.201254i
\(329\) 0.252302 + 0.776507i 0.0139099 + 0.0428102i
\(330\) 5.82387 13.0806i 0.320593 0.720065i
\(331\) 2.65508 12.4912i 0.145936 0.686577i −0.842961 0.537975i \(-0.819189\pi\)
0.988897 0.148602i \(-0.0474773\pi\)
\(332\) 3.49659 + 7.85347i 0.191900 + 0.431015i
\(333\) 10.5404 14.5076i 0.577609 0.795010i
\(334\) −5.04259 + 3.66366i −0.275918 + 0.200466i
\(335\) 1.28916 + 2.23290i 0.0704345 + 0.121996i
\(336\) 0.449205i 0.0245061i
\(337\) −0.353825 + 0.257069i −0.0192741 + 0.0140034i −0.597381 0.801958i \(-0.703792\pi\)
0.578107 + 0.815961i \(0.303792\pi\)
\(338\) −5.49124 12.5864i −0.298684 0.684611i
\(339\) −4.39027 13.5119i −0.238447 0.733864i
\(340\) 4.42915 + 2.55717i 0.240204 + 0.138682i
\(341\) 10.0969 + 1.12417i 0.546778 + 0.0608771i
\(342\) −0.462750 0.801507i −0.0250227 0.0433405i
\(343\) −1.92081 + 0.624110i −0.103714 + 0.0336988i
\(344\) 16.2360 + 5.27540i 0.875388 + 0.284431i
\(345\) −22.0885 + 49.6116i −1.18921 + 2.67100i
\(346\) −12.9224 + 7.46078i −0.694715 + 0.401094i
\(347\) 31.6938 1.70141 0.850705 0.525643i \(-0.176175\pi\)
0.850705 + 0.525643i \(0.176175\pi\)
\(348\) 7.11627 + 3.16837i 0.381472 + 0.169842i
\(349\) −7.88468 17.7093i −0.422057 0.947956i −0.991996 0.126269i \(-0.959700\pi\)
0.569939 0.821687i \(-0.306967\pi\)
\(350\) 0.111667 1.06244i 0.00596886 0.0567899i
\(351\) −8.74010 6.40021i −0.466512 0.341618i
\(352\) −7.60407 3.38555i −0.405299 0.180451i
\(353\) 10.1670 + 9.15438i 0.541133 + 0.487238i 0.893772 0.448521i \(-0.148049\pi\)
−0.352639 + 0.935759i \(0.614716\pi\)
\(354\) 6.64532 20.4522i 0.353195 1.08702i
\(355\) 22.0343 + 16.0088i 1.16946 + 0.849661i
\(356\) 10.4130 + 3.38338i 0.551886 + 0.179319i
\(357\) 0.107563 + 0.506042i 0.00569282 + 0.0267826i
\(358\) 14.9637 20.5958i 0.790858 1.08852i
\(359\) −5.90104 27.7622i −0.311445 1.46523i −0.803832 0.594857i \(-0.797209\pi\)
0.492387 0.870376i \(-0.336125\pi\)
\(360\) −5.21478 16.0494i −0.274843 0.845880i
\(361\) −15.1284 + 10.9914i −0.796233 + 0.578497i
\(362\) 9.01503 2.92916i 0.473819 0.153953i
\(363\) 1.71947 16.3597i 0.0902490 0.858662i
\(364\) 0.399745 0.228801i 0.0209523 0.0119924i
\(365\) 0.305266 + 2.90441i 0.0159783 + 0.152024i
\(366\) −5.63901 + 3.25568i −0.294756 + 0.170177i
\(367\) −3.85153 −0.201048 −0.100524 0.994935i \(-0.532052\pi\)
−0.100524 + 0.994935i \(0.532052\pi\)
\(368\) −9.68225 4.31082i −0.504722 0.224717i
\(369\) −1.49477 + 1.34590i −0.0778147 + 0.0700646i
\(370\) −30.4966 27.4593i −1.58544 1.42754i
\(371\) 1.63481 0.943857i 0.0848751 0.0490026i
\(372\) 8.57922 6.15276i 0.444812 0.319006i
\(373\) 0.320164 + 0.554541i 0.0165775 + 0.0287130i 0.874195 0.485575i \(-0.161390\pi\)
−0.857618 + 0.514288i \(0.828056\pi\)
\(374\) 3.14800 + 0.669127i 0.162779 + 0.0345997i
\(375\) 3.08906 + 14.5329i 0.159518 + 0.750475i
\(376\) 13.9289 10.1199i 0.718328 0.521896i
\(377\) 1.49310 + 14.7367i 0.0768988 + 0.758976i
\(378\) −0.229265 + 0.397098i −0.0117921 + 0.0204245i
\(379\) −4.92294 + 11.0571i −0.252874 + 0.567965i −0.994722 0.102603i \(-0.967283\pi\)
0.741848 + 0.670568i \(0.233950\pi\)
\(380\) 1.53322 0.682633i 0.0786525 0.0350183i
\(381\) 14.5091 6.45987i 0.743324 0.330949i
\(382\) 9.41013 + 8.47292i 0.481464 + 0.433512i
\(383\) −13.0903 + 1.37584i −0.668881 + 0.0703022i −0.432881 0.901451i \(-0.642503\pi\)
−0.236000 + 0.971753i \(0.575836\pi\)
\(384\) −1.97948 + 0.643172i −0.101015 + 0.0328217i
\(385\) 0.189867 + 0.893256i 0.00967654 + 0.0455245i
\(386\) −7.82164 5.68276i −0.398111 0.289245i
\(387\) −5.99528 6.65844i −0.304757 0.338467i
\(388\) 0.675247 0.607996i 0.0342805 0.0308663i
\(389\) 10.1324 4.51125i 0.513735 0.228729i −0.133460 0.991054i \(-0.542609\pi\)
0.647195 + 0.762325i \(0.275942\pi\)
\(390\) 19.0107 20.9552i 0.962645 1.06111i
\(391\) −11.9396 2.53783i −0.603810 0.128344i
\(392\) 12.4979 + 17.2019i 0.631242 + 0.868830i
\(393\) −3.61434 11.1238i −0.182319 0.561122i
\(394\) 21.0353 9.36553i 1.05974 0.471829i
\(395\) 4.84898 6.67405i 0.243979 0.335808i
\(396\) 1.51632 + 2.08704i 0.0761981 + 0.104878i
\(397\) 9.86375i 0.495048i −0.968882 0.247524i \(-0.920383\pi\)
0.968882 0.247524i \(-0.0796168\pi\)
\(398\) −18.0623 + 10.4283i −0.905381 + 0.522722i
\(399\) 0.155095 + 0.0690526i 0.00776445 + 0.00345696i
\(400\) −9.92695 + 2.11004i −0.496347 + 0.105502i
\(401\) −0.117067 + 0.550758i −0.00584606 + 0.0275036i −0.980974 0.194139i \(-0.937809\pi\)
0.975128 + 0.221643i \(0.0711419\pi\)
\(402\) 1.68606 0.0840931
\(403\) 18.2575 + 8.34646i 0.909471 + 0.415767i
\(404\) 1.98067 0.0985420
\(405\) 8.09549 38.0863i 0.402268 1.89252i
\(406\) 0.613258 0.130352i 0.0304355 0.00646926i
\(407\) 18.6941 + 8.32316i 0.926633 + 0.412564i
\(408\) 9.44785 5.45472i 0.467739 0.270049i
\(409\) 35.2963i 1.74529i 0.488356 + 0.872644i \(0.337597\pi\)
−0.488356 + 0.872644i \(0.662403\pi\)
\(410\) 2.70558 + 3.72391i 0.133619 + 0.183911i
\(411\) 6.65270 9.15666i 0.328154 0.451665i
\(412\) −7.84282 + 3.49185i −0.386388 + 0.172031i
\(413\) 0.423827 + 1.30441i 0.0208552 + 0.0641857i
\(414\) 7.25754 + 9.98915i 0.356689 + 0.490940i
\(415\) −32.9443 7.00252i −1.61717 0.343740i
\(416\) −12.1817 11.0514i −0.597259 0.541838i
\(417\) −38.4215 + 17.1064i −1.88151 + 0.837702i
\(418\) 0.784852 0.706684i 0.0383884 0.0345650i
\(419\) −14.3566 15.9446i −0.701364 0.778944i 0.282229 0.959347i \(-0.408926\pi\)
−0.983593 + 0.180403i \(0.942260\pi\)
\(420\) 0.767758 + 0.557809i 0.0374627 + 0.0272183i
\(421\) −7.28010 34.2502i −0.354810 1.66925i −0.687476 0.726207i \(-0.741281\pi\)
0.332665 0.943045i \(-0.392052\pi\)
\(422\) −18.5483 + 6.02670i −0.902916 + 0.293375i
\(423\) −8.98667 + 0.944537i −0.436947 + 0.0459250i
\(424\) −29.5822 26.6359i −1.43664 1.29355i
\(425\) −10.6778 + 4.75404i −0.517947 + 0.230605i
\(426\) 16.2707 7.24420i 0.788319 0.350982i
\(427\) 0.168911 0.379381i 0.00817419 0.0183595i
\(428\) 3.82127 6.61864i 0.184708 0.319924i
\(429\) −5.78673 + 12.8673i −0.279386 + 0.621239i
\(430\) −16.5881 + 12.0520i −0.799950 + 0.581198i
\(431\) −5.34041 25.1246i −0.257238 1.21021i −0.897137 0.441752i \(-0.854357\pi\)
0.639899 0.768459i \(-0.278976\pi\)
\(432\) 4.26081 + 0.905664i 0.204998 + 0.0435738i
\(433\) −12.3819 21.4461i −0.595038 1.03064i −0.993542 0.113469i \(-0.963804\pi\)
0.398504 0.917167i \(-0.369530\pi\)
\(434\) 0.267551 0.806496i 0.0128429 0.0387130i
\(435\) −26.4300 + 15.2594i −1.26722 + 0.731630i
\(436\) 11.4432 + 10.3035i 0.548032 + 0.493450i
\(437\) −2.97675 + 2.68028i −0.142397 + 0.128215i
\(438\) 1.74465 + 0.776770i 0.0833627 + 0.0371155i
\(439\) −27.7277 −1.32337 −0.661686 0.749781i \(-0.730159\pi\)
−0.661686 + 0.749781i \(0.730159\pi\)
\(440\) 16.6772 9.62856i 0.795052 0.459024i
\(441\) −1.16649 11.0984i −0.0555470 0.528495i
\(442\) 5.49549 + 3.20033i 0.261394 + 0.152224i
\(443\) −3.35621 + 31.9322i −0.159458 + 1.51715i 0.563420 + 0.826171i \(0.309485\pi\)
−0.722878 + 0.690975i \(0.757181\pi\)
\(444\) 20.2244 6.57132i 0.959810 0.311861i
\(445\) −34.7032 + 25.2134i −1.64509 + 1.19523i
\(446\) −5.27300 16.2286i −0.249684 0.768447i
\(447\) 3.39263 + 15.9610i 0.160466 + 0.754932i
\(448\) −0.655452 + 0.902152i −0.0309672 + 0.0426227i
\(449\) −7.16095 33.6896i −0.337946 1.58991i −0.738901 0.673814i \(-0.764655\pi\)
0.400955 0.916098i \(-0.368678\pi\)
\(450\) 11.2446 + 3.65358i 0.530074 + 0.172231i
\(451\) −1.85693 1.34914i −0.0874396 0.0635286i
\(452\) 1.81012 5.57097i 0.0851408 0.262036i
\(453\) −12.3782 11.1454i −0.581579 0.523656i
\(454\) 16.3080 + 7.26080i 0.765374 + 0.340766i
\(455\) −0.195343 + 1.79391i −0.00915784 + 0.0840999i
\(456\) 0.374215 3.56042i 0.0175242 0.166732i
\(457\) 11.0116 + 24.7325i 0.515103 + 1.15694i 0.964614 + 0.263665i \(0.0849314\pi\)
−0.449512 + 0.893275i \(0.648402\pi\)
\(458\) −12.4740 5.55379i −0.582873 0.259512i
\(459\) 5.01679 0.234164
\(460\) −19.3910 + 11.1954i −0.904108 + 0.521987i
\(461\) 1.79742 4.03708i 0.0837143 0.188025i −0.866838 0.498590i \(-0.833851\pi\)
0.950552 + 0.310564i \(0.100518\pi\)
\(462\) 0.567954 + 0.184539i 0.0264236 + 0.00858555i
\(463\) 30.2425 9.82640i 1.40549 0.456671i 0.494528 0.869162i \(-0.335341\pi\)
0.910962 + 0.412490i \(0.135341\pi\)
\(464\) −2.97803 5.15810i −0.138252 0.239459i
\(465\) −0.254851 + 41.3613i −0.0118184 + 1.91808i
\(466\) −10.3555 5.97877i −0.479711 0.276961i
\(467\) 4.21698 + 12.9785i 0.195138 + 0.600574i 0.999975 + 0.00707768i \(0.00225291\pi\)
−0.804837 + 0.593496i \(0.797747\pi\)
\(468\) 1.55707 + 4.85394i 0.0719754 + 0.224373i
\(469\) −0.0869969 + 0.0632070i −0.00401714 + 0.00291863i
\(470\) 20.6788i 0.953842i
\(471\) 15.4359 + 26.7358i 0.711251 + 1.23192i
\(472\) 23.3983 16.9999i 1.07699 0.782482i
\(473\) 6.00973 8.27169i 0.276328 0.380333i
\(474\) −2.19422 4.92830i −0.100784 0.226364i
\(475\) −0.797468 + 3.75179i −0.0365903 + 0.172144i
\(476\) −0.0867583 + 0.194862i −0.00397656 + 0.00893150i
\(477\) 6.45601 + 19.8696i 0.295601 + 0.909765i
\(478\) −5.41497 + 16.6656i −0.247675 + 0.762266i
\(479\) 21.0953 + 2.21720i 0.963867 + 0.101306i 0.573369 0.819297i \(-0.305636\pi\)
0.390498 + 0.920604i \(0.372303\pi\)
\(480\) 10.4722 32.2301i 0.477988 1.47110i
\(481\) 29.9480 + 27.1691i 1.36551 + 1.23880i
\(482\) 16.9924 7.56552i 0.773984 0.344600i
\(483\) −2.15411 0.699913i −0.0980154 0.0318471i
\(484\) 4.53824 5.04023i 0.206284 0.229101i
\(485\) 0.372107 + 3.54036i 0.0168965 + 0.160760i
\(486\) −11.8467 10.6668i −0.537376 0.483856i
\(487\) −0.491341 1.10357i −0.0222648 0.0500076i 0.902071 0.431588i \(-0.142047\pi\)
−0.924336 + 0.381580i \(0.875380\pi\)
\(488\) −8.70923 0.915377i −0.394248 0.0414372i
\(489\) −1.81008 + 0.190247i −0.0818547 + 0.00860327i
\(490\) −25.5380 −1.15369
\(491\) −18.5936 −0.839117 −0.419559 0.907728i \(-0.637815\pi\)
−0.419559 + 0.907728i \(0.637815\pi\)
\(492\) −2.37218 + 0.249327i −0.106946 + 0.0112405i
\(493\) −4.58996 5.09766i −0.206721 0.229587i
\(494\) 1.90965 0.841676i 0.0859193 0.0378688i
\(495\) −10.1069 −0.454270
\(496\) −8.07211 0.0497370i −0.362448 0.00223326i
\(497\) −0.567963 + 0.983740i −0.0254766 + 0.0441268i
\(498\) −14.7374 + 16.3676i −0.660400 + 0.733448i
\(499\) 7.54833 6.79655i 0.337910 0.304255i −0.482653 0.875812i \(-0.660327\pi\)
0.820563 + 0.571556i \(0.193660\pi\)
\(500\) −2.49159 + 5.59620i −0.111427 + 0.250270i
\(501\) 10.9588 + 6.32707i 0.489603 + 0.282672i
\(502\) 11.5950 + 6.69436i 0.517509 + 0.298784i
\(503\) −6.74929 + 4.90364i −0.300936 + 0.218643i −0.727997 0.685580i \(-0.759549\pi\)
0.427062 + 0.904223i \(0.359549\pi\)
\(504\) 0.642972 0.286270i 0.0286403 0.0127515i
\(505\) −4.56115 + 6.27789i −0.202969 + 0.279362i
\(506\) −9.42800 + 10.4709i −0.419126 + 0.465486i
\(507\) −18.8092 + 20.5777i −0.835347 + 0.913887i
\(508\) 6.40516 + 1.36146i 0.284183 + 0.0604050i
\(509\) −13.6548 4.43671i −0.605238 0.196654i −0.00966294 0.999953i \(-0.503076\pi\)
−0.595575 + 0.803299i \(0.703076\pi\)
\(510\) −1.36963 + 13.0312i −0.0606482 + 0.577029i
\(511\) −0.119140 + 0.0253239i −0.00527043 + 0.00112026i
\(512\) 14.6918 + 4.77366i 0.649292 + 0.210968i
\(513\) 0.967675 1.33189i 0.0427239 0.0588044i
\(514\) 18.0723 16.2724i 0.797135 0.717743i
\(515\) 6.99302 32.8996i 0.308149 1.44973i
\(516\) −1.11062 10.5669i −0.0488924 0.465180i
\(517\) −3.18643 9.80683i −0.140139 0.431304i
\(518\) 1.00602 1.38466i 0.0442018 0.0608386i
\(519\) 24.5080 + 17.8061i 1.07578 + 0.781601i
\(520\) 37.2501 7.77206i 1.63353 0.340827i
\(521\) 12.9656 22.4571i 0.568034 0.983864i −0.428726 0.903434i \(-0.641038\pi\)
0.996760 0.0804292i \(-0.0256291\pi\)
\(522\) 6.93880i 0.303703i
\(523\) −1.39293 13.2528i −0.0609086 0.579507i −0.981831 0.189760i \(-0.939229\pi\)
0.920922 0.389747i \(-0.127438\pi\)
\(524\) 1.49020 4.58637i 0.0650997 0.200356i
\(525\) −2.06269 + 0.670207i −0.0900230 + 0.0292502i
\(526\) −4.36834 + 2.52206i −0.190468 + 0.109967i
\(527\) −9.10538 + 1.87685i −0.396637 + 0.0817567i
\(528\) 5.67319i 0.246894i
\(529\) 20.3681 22.6211i 0.885569 0.983525i
\(530\) 46.7657 9.94035i 2.03137 0.431781i
\(531\) −15.0962 + 1.58667i −0.655118 + 0.0688557i
\(532\) 0.0349987 + 0.0606196i 0.00151739 + 0.00262819i
\(533\) −2.65216 3.67928i −0.114878 0.159367i
\(534\) 2.93212 + 27.8973i 0.126885 + 1.20723i
\(535\) 12.1785 + 27.3534i 0.526524 + 1.18259i
\(536\) 1.83453 + 1.33286i 0.0792395 + 0.0575708i
\(537\) −50.5547 10.7457i −2.18160 0.463713i
\(538\) −7.77666 + 17.4667i −0.335276 + 0.753041i
\(539\) 12.1113 3.93519i 0.521669 0.169501i
\(540\) 6.83886 6.15774i 0.294298 0.264987i
\(541\) −9.45364 21.2332i −0.406444 0.912887i −0.994565 0.104115i \(-0.966799\pi\)
0.588122 0.808772i \(-0.299868\pi\)
\(542\) 15.2482 3.24110i 0.654966 0.139217i
\(543\) −12.8768 14.3011i −0.552596 0.613720i
\(544\) 7.57532 + 0.796198i 0.324789 + 0.0341367i
\(545\) −59.0097 + 12.5429i −2.52770 + 0.537279i
\(546\) 0.952067 + 0.697180i 0.0407447 + 0.0298365i
\(547\) 4.25547 + 1.89466i 0.181951 + 0.0810096i 0.495690 0.868499i \(-0.334915\pi\)
−0.313740 + 0.949509i \(0.601582\pi\)
\(548\) 4.43814 1.44204i 0.189588 0.0616009i
\(549\) 3.71834 + 2.70153i 0.158695 + 0.115298i
\(550\) −1.41029 + 13.4180i −0.0601350 + 0.572146i
\(551\) −2.23870 + 0.235297i −0.0953720 + 0.0100240i
\(552\) 47.7619i 2.03288i
\(553\) 0.297969 + 0.172032i 0.0126709 + 0.00731556i
\(554\) −14.1596 19.4889i −0.601582 0.828006i
\(555\) −25.7452 + 79.2356i −1.09282 + 3.36336i
\(556\) −16.9615 3.60528i −0.719328 0.152898i
\(557\) 21.2632 + 12.2763i 0.900949 + 0.520163i 0.877508 0.479562i \(-0.159204\pi\)
0.0234413 + 0.999725i \(0.492538\pi\)
\(558\) 8.11512 + 4.75217i 0.343540 + 0.201175i
\(559\) 16.3893 11.8140i 0.693194 0.499679i
\(560\) −0.224226 0.690097i −0.00947528 0.0291619i
\(561\) −1.35845 6.39102i −0.0573540 0.269829i
\(562\) −2.98933 28.4416i −0.126097 1.19974i
\(563\) 16.6429 28.8263i 0.701414 1.21488i −0.266556 0.963819i \(-0.585886\pi\)
0.967970 0.251065i \(-0.0807809\pi\)
\(564\) −9.28001 5.35781i −0.390759 0.225605i
\(565\) 13.4892 + 18.5663i 0.567496 + 0.781091i
\(566\) 0.594891 + 0.0625255i 0.0250051 + 0.00262814i
\(567\) 1.61505 + 0.169749i 0.0678259 + 0.00712879i
\(568\) 23.4301 + 4.98022i 0.983106 + 0.208966i
\(569\) 16.2618 11.8149i 0.681728 0.495305i −0.192202 0.981355i \(-0.561563\pi\)
0.873931 + 0.486051i \(0.161563\pi\)
\(570\) 3.19541 + 2.87716i 0.133841 + 0.120511i
\(571\) 39.7054 8.43965i 1.66162 0.353188i 0.721075 0.692857i \(-0.243648\pi\)
0.940545 + 0.339669i \(0.110315\pi\)
\(572\) −5.04854 + 2.88962i −0.211090 + 0.120821i
\(573\) 7.94403 24.4492i 0.331867 1.02138i
\(574\) −0.142667 + 0.128458i −0.00595481 + 0.00536173i
\(575\) 5.34889 50.8912i 0.223064 2.12231i
\(576\) −8.25807 9.17152i −0.344086 0.382147i
\(577\) −3.23258 + 15.2081i −0.134574 + 0.633120i 0.858220 + 0.513283i \(0.171571\pi\)
−0.992793 + 0.119838i \(0.961763\pi\)
\(578\) 14.9301 1.56921i 0.621009 0.0652707i
\(579\) −4.08090 + 19.1991i −0.169596 + 0.797887i
\(580\) −12.5140 1.31527i −0.519615 0.0546138i
\(581\) 0.146831 1.39701i 0.00609158 0.0579576i
\(582\) 2.12666 + 0.946852i 0.0881531 + 0.0392483i
\(583\) −20.6467 + 11.9204i −0.855099 + 0.493691i
\(584\) 1.28423 + 2.22435i 0.0531417 + 0.0920442i
\(585\) −18.9706 6.24257i −0.784338 0.258098i
\(586\) −9.89736 10.9921i −0.408856 0.454081i
\(587\) 8.38491 39.4479i 0.346082 1.62819i −0.369198 0.929351i \(-0.620367\pi\)
0.715280 0.698838i \(-0.246299\pi\)
\(588\) 6.61681 11.4606i 0.272873 0.472629i
\(589\) −1.25803 + 2.77937i −0.0518364 + 0.114522i
\(590\) 34.7371i 1.43010i
\(591\) −34.7399 31.2800i −1.42901 1.28669i
\(592\) −15.4637 5.02446i −0.635554 0.206504i
\(593\) 1.83738 + 2.52894i 0.0754523 + 0.103851i 0.845075 0.534648i \(-0.179556\pi\)
−0.769623 + 0.638499i \(0.779556\pi\)
\(594\) 2.89548 5.01512i 0.118803 0.205773i
\(595\) −0.417842 0.723723i −0.0171298 0.0296698i
\(596\) −2.73644 + 6.14614i −0.112089 + 0.251756i
\(597\) 34.2560 + 24.8884i 1.40200 + 1.01861i
\(598\) −24.1637 + 13.8305i −0.988128 + 0.565572i
\(599\) −4.68333 + 5.20137i −0.191356 + 0.212522i −0.831186 0.555994i \(-0.812338\pi\)
0.639831 + 0.768516i \(0.279004\pi\)
\(600\) 26.8822 + 37.0002i 1.09746 + 1.51053i
\(601\) −7.96616 + 8.84732i −0.324946 + 0.360890i −0.883378 0.468661i \(-0.844737\pi\)
0.558432 + 0.829550i \(0.311403\pi\)
\(602\) −0.572214 0.635509i −0.0233217 0.0259014i
\(603\) −0.484067 1.08723i −0.0197127 0.0442755i
\(604\) −1.42784 6.71744i −0.0580978 0.273329i
\(605\) 5.52458 + 25.9911i 0.224606 + 1.05669i
\(606\) 2.06398 + 4.63577i 0.0838433 + 0.188315i
\(607\) −2.99049 3.32128i −0.121380 0.134807i 0.679392 0.733776i \(-0.262244\pi\)
−0.800772 + 0.598969i \(0.795577\pi\)
\(608\) 1.67256 1.85757i 0.0678313 0.0753343i
\(609\) −0.748158 1.02975i −0.0303169 0.0417276i
\(610\) 7.03789 7.81637i 0.284956 0.316475i
\(611\) 0.0763124 20.3755i 0.00308727 0.824305i
\(612\) −1.90986 1.38759i −0.0772015 0.0560902i
\(613\) −17.2186 + 38.6736i −0.695453 + 1.56201i 0.126187 + 0.992006i \(0.459726\pi\)
−0.821640 + 0.570007i \(0.806941\pi\)
\(614\) −11.7285 20.3144i −0.473324 0.819821i
\(615\) 4.67249 8.09298i 0.188413 0.326341i
\(616\) 0.472083 + 0.649767i 0.0190208 + 0.0261799i
\(617\) 27.1885 + 8.83408i 1.09457 + 0.355647i 0.800010 0.599987i \(-0.204828\pi\)
0.294558 + 0.955634i \(0.404828\pi\)
\(618\) −16.3454 14.7174i −0.657507 0.592022i
\(619\) 3.44047i 0.138284i 0.997607 + 0.0691421i \(0.0220262\pi\)
−0.997607 + 0.0691421i \(0.977974\pi\)
\(620\) −10.1087 + 13.7347i −0.405976 + 0.551598i
\(621\) −10.9818 + 19.0211i −0.440686 + 0.763291i
\(622\) −0.737948 + 3.47177i −0.0295890 + 0.139205i
\(623\) −1.19710 1.32952i −0.0479609 0.0532660i
\(624\) 3.50408 10.6486i 0.140275 0.426284i
\(625\) 5.50008 + 9.52642i 0.220003 + 0.381057i
\(626\) −8.87172 + 5.12209i −0.354585 + 0.204720i
\(627\) −1.95876 0.872095i −0.0782252 0.0348281i
\(628\) −1.33050 + 12.6588i −0.0530925 + 0.505142i
\(629\) −18.6234 1.95740i −0.742565 0.0780467i
\(630\) −0.175755 + 0.826861i −0.00700224 + 0.0329429i
\(631\) −0.0539352 + 0.00566882i −0.00214713 + 0.000225672i −0.105602 0.994408i \(-0.533677\pi\)
0.103455 + 0.994634i \(0.467010\pi\)
\(632\) 1.50848 7.09684i 0.0600041 0.282297i
\(633\) 26.4938 + 29.4243i 1.05303 + 1.16951i
\(634\) 1.60897 15.3083i 0.0639003 0.607971i
\(635\) −19.0653 + 17.1664i −0.756582 + 0.681230i
\(636\) −7.65592 + 23.5625i −0.303577 + 0.934314i
\(637\) 25.1634 + 0.0942445i 0.997011 + 0.00373410i
\(638\) −7.74509 + 1.64627i −0.306631 + 0.0651764i
\(639\) −9.34263 8.41214i −0.369589 0.332779i
\(640\) 2.71995 1.97616i 0.107516 0.0781147i
\(641\) −14.3343 3.04684i −0.566169 0.120343i −0.0840703 0.996460i \(-0.526792\pi\)
−0.482099 + 0.876117i \(0.660125\pi\)
\(642\) 19.4730 + 2.04669i 0.768536 + 0.0807764i
\(643\) 23.0540 + 2.42308i 0.909163 + 0.0955568i 0.547551 0.836772i \(-0.315560\pi\)
0.361611 + 0.932329i \(0.382227\pi\)
\(644\) −0.548903 0.755500i −0.0216298 0.0297709i
\(645\) 36.0501 + 20.8135i 1.41947 + 0.819532i
\(646\) −0.483231 + 0.836980i −0.0190125 + 0.0329305i
\(647\) 0.365145 + 3.47412i 0.0143553 + 0.136582i 0.999352 0.0359909i \(-0.0114587\pi\)
−0.984997 + 0.172573i \(0.944792\pi\)
\(648\) −7.11987 33.4963i −0.279695 1.31586i
\(649\) −5.35270 16.4739i −0.210112 0.646657i
\(650\) −10.9348 + 24.3145i −0.428899 + 0.953694i
\(651\) −1.71671 + 0.169746i −0.0672833 + 0.00665288i
\(652\) −0.649875 0.375205i −0.0254511 0.0146942i
\(653\) −35.7396 7.59669i −1.39860 0.297281i −0.553927 0.832566i \(-0.686871\pi\)
−0.844672 + 0.535284i \(0.820205\pi\)
\(654\) −12.1909 + 37.5198i −0.476703 + 1.46714i
\(655\) 11.1052 + 15.2849i 0.433915 + 0.597232i
\(656\) 1.57943 + 0.911887i 0.0616666 + 0.0356032i
\(657\) 1.34802i 0.0525914i
\(658\) −0.857725 + 0.0901505i −0.0334376 + 0.00351443i
\(659\) −1.32278 + 12.5854i −0.0515280 + 0.490256i 0.938075 + 0.346432i \(0.112607\pi\)
−0.989603 + 0.143824i \(0.954060\pi\)
\(660\) −9.69634 7.04480i −0.377429 0.274219i
\(661\) 26.4244 8.58580i 1.02779 0.333949i 0.253873 0.967238i \(-0.418295\pi\)
0.773916 + 0.633289i \(0.218295\pi\)
\(662\) 12.3232 + 5.48665i 0.478955 + 0.213245i
\(663\) 1.39763 12.8350i 0.0542796 0.498470i
\(664\) −28.9740 + 6.15861i −1.12441 + 0.239000i
\(665\) −0.272735 0.0286656i −0.0105762 0.00111160i
\(666\) 12.6749 + 14.0769i 0.491141 + 0.545467i
\(667\) 29.3752 6.24390i 1.13741 0.241765i
\(668\) 2.12208 + 4.76626i 0.0821056 + 0.184412i
\(669\) −25.7445 + 23.1805i −0.995341 + 0.896209i
\(670\) −2.59023 + 0.841618i −0.100069 + 0.0325145i
\(671\) −2.13325 + 4.79136i −0.0823532 + 0.184968i
\(672\) 1.38251 + 0.293862i 0.0533315 + 0.0113360i
\(673\) 35.8888 + 26.0747i 1.38341 + 1.00511i 0.996552 + 0.0829669i \(0.0264396\pi\)
0.386858 + 0.922139i \(0.373560\pi\)
\(674\) −0.187905 0.422042i −0.00723784 0.0162565i
\(675\) 2.19839 + 20.9163i 0.0846162 + 0.805069i
\(676\) −11.2609 + 2.30555i −0.433111 + 0.0886752i
\(677\) −16.0776 27.8471i −0.617911 1.07025i −0.989866 0.142002i \(-0.954646\pi\)
0.371956 0.928251i \(-0.378687\pi\)
\(678\) 14.9251 1.56869i 0.573196 0.0602453i
\(679\) −0.145227 + 0.0308689i −0.00557329 + 0.00118464i
\(680\) −11.7916 + 13.0959i −0.452187 + 0.502205i
\(681\) 36.2416i 1.38878i
\(682\) −3.37902 + 10.1856i −0.129389 + 0.390026i
\(683\) 11.7370 6.77634i 0.449102 0.259289i −0.258349 0.966052i \(-0.583178\pi\)
0.707451 + 0.706762i \(0.249845\pi\)
\(684\) −0.736774 + 0.239392i −0.0281713 + 0.00915340i
\(685\) −5.64965 + 17.3878i −0.215862 + 0.664354i
\(686\) −0.223002 2.12172i −0.00851424 0.0810076i
\(687\) 27.7212i 1.05763i
\(688\) −4.06199 + 7.03557i −0.154862 + 0.268229i
\(689\) −46.1165 + 9.62198i −1.75690 + 0.366568i
\(690\) −46.4094 33.7184i −1.76677 1.28364i
\(691\) −13.8797 + 19.1038i −0.528008 + 0.726741i −0.986825 0.161790i \(-0.948273\pi\)
0.458817 + 0.888531i \(0.348273\pi\)
\(692\) 3.85965 + 11.8788i 0.146722 + 0.451564i
\(693\) −0.0440616 0.419218i −0.00167376 0.0159248i
\(694\) −6.96061 + 32.7471i −0.264221 + 1.24306i
\(695\) 50.4867 45.4584i 1.91507 1.72434i
\(696\) −15.7766 + 21.7146i −0.598011 + 0.823091i
\(697\) 1.99763 + 0.649070i 0.0756657 + 0.0245853i
\(698\) 20.0295 4.25740i 0.758127 0.161145i
\(699\) −2.53754 + 24.1431i −0.0959786 + 0.913175i
\(700\) −0.850450 0.276328i −0.0321440 0.0104442i
\(701\) 1.81235 + 0.385228i 0.0684517 + 0.0145499i 0.242010 0.970274i \(-0.422193\pi\)
−0.173559 + 0.984824i \(0.555527\pi\)
\(702\) 8.53243 7.62496i 0.322036 0.287786i
\(703\) −4.11188 + 4.56671i −0.155083 + 0.172237i
\(704\) 8.27798 11.3937i 0.311988 0.429415i
\(705\) 38.3523 17.0756i 1.44443 0.643103i
\(706\) −11.6915 + 8.49437i −0.440015 + 0.319690i
\(707\) −0.280282 0.161821i −0.0105411 0.00608590i
\(708\) −15.5889 9.00027i −0.585868 0.338251i
\(709\) 10.7170 24.0708i 0.402485 0.903997i −0.592648 0.805461i \(-0.701918\pi\)
0.995134 0.0985355i \(-0.0314158\pi\)
\(710\) −21.3801 + 19.2507i −0.802381 + 0.722467i
\(711\) −2.54799 + 2.82982i −0.0955569 + 0.106127i
\(712\) −18.8630 + 32.6717i −0.706921 + 1.22442i
\(713\) 12.8158 38.6314i 0.479955 1.44676i
\(714\) −0.546484 −0.0204516
\(715\) 2.46707 22.6561i 0.0922633 0.847289i
\(716\) −14.2588 15.8360i −0.532877 0.591820i
\(717\) 35.3806 3.71865i 1.32131 0.138875i
\(718\) 29.9809 1.11888
\(719\) −42.3088 −1.57785 −0.788926 0.614488i \(-0.789362\pi\)
−0.788926 + 0.614488i \(0.789362\pi\)
\(720\) 7.98663 0.839429i 0.297644 0.0312837i
\(721\) 1.39511 + 0.146632i 0.0519566 + 0.00546086i
\(722\) −8.03423 18.0452i −0.299003 0.671572i
\(723\) −28.0631 25.2681i −1.04368 0.939730i
\(724\) −0.829368 7.89091i −0.0308232 0.293263i
\(725\) 19.2421 21.3705i 0.714634 0.793682i
\(726\) 16.5258 + 5.36955i 0.613329 + 0.199283i
\(727\) −40.2678 + 17.9284i −1.49345 + 0.664927i −0.981038 0.193814i \(-0.937914\pi\)
−0.512411 + 0.858740i \(0.671248\pi\)
\(728\) 0.484768 + 1.51120i 0.0179667 + 0.0560087i
\(729\) 0.419280 1.29041i 0.0155289 0.0477930i
\(730\) −3.06798 0.322458i −0.113551 0.0119347i
\(731\) −2.89128 + 8.89843i −0.106938 + 0.329120i
\(732\) 1.68425 + 5.18359i 0.0622516 + 0.191591i
\(733\) −11.1850 + 25.1219i −0.413126 + 0.927897i 0.580404 + 0.814329i \(0.302895\pi\)
−0.993530 + 0.113568i \(0.963772\pi\)
\(734\) 0.845878 3.97954i 0.0312219 0.146888i
\(735\) 21.0880 + 47.3645i 0.777843 + 1.74706i
\(736\) −19.6013 + 26.9788i −0.722513 + 0.994454i
\(737\) 1.09872 0.798267i 0.0404719 0.0294046i
\(738\) −1.06235 1.84004i −0.0391055 0.0677327i
\(739\) 53.3000i 1.96067i −0.197335 0.980336i \(-0.563229\pi\)
0.197335 0.980336i \(-0.436771\pi\)
\(740\) −27.7899 + 20.1906i −1.02158 + 0.742220i
\(741\) −3.13793 2.84676i −0.115275 0.104578i
\(742\) 0.616188 + 1.89643i 0.0226210 + 0.0696202i
\(743\) 37.3023 + 21.5365i 1.36849 + 0.790097i 0.990735 0.135810i \(-0.0433635\pi\)
0.377753 + 0.925906i \(0.376697\pi\)
\(744\) 14.5910 + 33.3229i 0.534930 + 1.22168i
\(745\) −13.1791 22.8269i −0.482846 0.836313i
\(746\) −0.643286 + 0.209016i −0.0235524 + 0.00765262i
\(747\) 14.7855 + 4.80410i 0.540973 + 0.175773i
\(748\) 1.09571 2.46100i 0.0400630 0.0899831i
\(749\) −1.08149 + 0.624396i −0.0395167 + 0.0228149i
\(750\) −15.6943 −0.573075
\(751\) 12.6722 + 5.64204i 0.462416 + 0.205881i 0.624702 0.780863i \(-0.285220\pi\)
−0.162287 + 0.986744i \(0.551887\pi\)
\(752\) 3.33248 + 7.48488i 0.121523 + 0.272945i
\(753\) 2.84125 27.0327i 0.103541 0.985127i
\(754\) −15.5543 1.69375i −0.566456 0.0616827i
\(755\) 24.5795 + 10.9435i 0.894540 + 0.398275i
\(756\) 0.285228 + 0.256821i 0.0103736 + 0.00934048i
\(757\) −1.78552 + 5.49527i −0.0648959 + 0.199729i −0.978247 0.207444i \(-0.933485\pi\)
0.913351 + 0.407173i \(0.133485\pi\)
\(758\) −10.3434 7.51492i −0.375689 0.272954i
\(759\) 27.2052 + 8.83949i 0.987485 + 0.320853i
\(760\) 1.20233 + 5.65654i 0.0436133 + 0.205184i
\(761\) −16.3110 + 22.4502i −0.591274 + 0.813819i −0.994875 0.101116i \(-0.967759\pi\)
0.403600 + 0.914935i \(0.367759\pi\)
\(762\) 3.48806 + 16.4100i 0.126359 + 0.594473i
\(763\) −0.777517 2.39295i −0.0281480 0.0866307i
\(764\) 8.57495 6.23007i 0.310231 0.225396i
\(765\) 8.79617 2.85805i 0.318026 0.103333i
\(766\) 1.45333 13.8275i 0.0525108 0.499607i
\(767\) 0.128193 34.2276i 0.00462876 1.23589i
\(768\) −3.69015 35.1095i −0.133157 1.26690i
\(769\) 27.9715 16.1493i 1.00868 0.582360i 0.0978728 0.995199i \(-0.468796\pi\)
0.910804 + 0.412839i \(0.135463\pi\)
\(770\) −0.964642 −0.0347633
\(771\) −45.1031 20.0812i −1.62435 0.723206i
\(772\) −6.01403 + 5.41506i −0.216450 + 0.194892i
\(773\) −11.8021 10.6267i −0.424493 0.382215i 0.429013 0.903298i \(-0.358861\pi\)
−0.853506 + 0.521083i \(0.825528\pi\)
\(774\) 8.19642 4.73221i 0.294614 0.170096i
\(775\) −11.8151 37.1402i −0.424411 1.33412i
\(776\) 1.56542 + 2.71139i 0.0561954 + 0.0973334i
\(777\) −3.39881 0.722440i −0.121932 0.0259174i
\(778\) 2.43589 + 11.4599i 0.0873308 + 0.410859i
\(779\) 0.557637 0.405147i 0.0199794 0.0145159i
\(780\) −13.8487 19.2121i −0.495865 0.687903i
\(781\) 7.17304 12.4241i 0.256672 0.444568i
\(782\) 5.24436 11.7790i 0.187538 0.421217i
\(783\) −11.2758 + 5.02033i −0.402966 + 0.179412i
\(784\) −9.24370 + 4.11556i −0.330132 + 0.146984i
\(785\) −37.0592 33.3682i −1.32270 1.19096i
\(786\) 12.2873 1.29145i 0.438273 0.0460644i
\(787\) −48.5050 + 15.7602i −1.72902 + 0.561792i −0.993307 0.115505i \(-0.963151\pi\)
−0.735710 + 0.677297i \(0.763151\pi\)
\(788\) −4.00728 18.8528i −0.142753 0.671602i
\(789\) 8.28475 + 6.01922i 0.294945 + 0.214290i
\(790\) 5.83093 + 6.47590i 0.207455 + 0.230402i
\(791\) −0.711296 + 0.640454i −0.0252908 + 0.0227719i
\(792\) −8.12037 + 3.61542i −0.288545 + 0.128468i
\(793\) −6.96352 + 7.67576i −0.247282 + 0.272574i
\(794\) 10.1916 + 2.16629i 0.361685 + 0.0768786i
\(795\) −57.0529 78.5266i −2.02346 2.78505i
\(796\) 5.39481 + 16.6035i 0.191214 + 0.588496i
\(797\) 14.1236 6.28821i 0.500282 0.222740i −0.141051 0.990002i \(-0.545048\pi\)
0.641333 + 0.767262i \(0.278382\pi\)
\(798\) −0.105410 + 0.145084i −0.00373146 + 0.00513592i
\(799\) 5.54640 + 7.63397i 0.196218 + 0.270070i
\(800\) 31.9324i 1.12898i
\(801\) 17.1473 9.90002i 0.605872 0.349800i
\(802\) −0.543353 0.241916i −0.0191864 0.00854236i
\(803\) 1.50466 0.319826i 0.0530985 0.0112864i
\(804\) 0.293430 1.38048i 0.0103485 0.0486857i
\(805\) 3.65865 0.128950
\(806\) −12.6336 + 17.0312i −0.444999 + 0.599900i
\(807\) 38.8165 1.36640
\(808\) −1.41894 + 6.67558i −0.0499181 + 0.234846i
\(809\) 27.6866 5.88497i 0.973410 0.206905i 0.306358 0.951916i \(-0.400889\pi\)
0.667051 + 0.745012i \(0.267556\pi\)
\(810\) 37.5742 + 16.7291i 1.32022 + 0.587801i
\(811\) −13.7054 + 7.91284i −0.481263 + 0.277857i −0.720943 0.692995i \(-0.756291\pi\)
0.239680 + 0.970852i \(0.422958\pi\)
\(812\) 0.524796i 0.0184167i
\(813\) −18.6024 25.6040i −0.652415 0.897972i
\(814\) −12.7054 + 17.4875i −0.445324 + 0.612936i
\(815\) 2.68580 1.19579i 0.0940793 0.0418868i
\(816\) 1.60428 + 4.93747i 0.0561611 + 0.172846i
\(817\) 1.80472 + 2.48399i 0.0631392 + 0.0869037i
\(818\) −36.4694 7.75180i −1.27512 0.271035i
\(819\) 0.176229 0.814086i 0.00615793 0.0284465i
\(820\) 3.51985 1.56714i 0.122918 0.0547268i
\(821\) −13.4094 + 12.0739i −0.467990 + 0.421380i −0.869090 0.494654i \(-0.835295\pi\)
0.401100 + 0.916034i \(0.368628\pi\)
\(822\) 7.99991 + 8.88480i 0.279029 + 0.309893i
\(823\) −36.6305 26.6136i −1.27686 0.927693i −0.277406 0.960753i \(-0.589475\pi\)
−0.999453 + 0.0330598i \(0.989475\pi\)
\(824\) −6.15026 28.9347i −0.214254 1.00799i
\(825\) 26.0505 8.46433i 0.906963 0.294690i
\(826\) −1.44084 + 0.151438i −0.0501332 + 0.00526922i
\(827\) 12.7692 + 11.4975i 0.444030 + 0.399806i 0.860587 0.509303i \(-0.170097\pi\)
−0.416557 + 0.909109i \(0.636764\pi\)
\(828\) 9.44176 4.20374i 0.328124 0.146090i
\(829\) 45.4202 20.2224i 1.57751 0.702352i 0.583547 0.812080i \(-0.301665\pi\)
0.993962 + 0.109728i \(0.0349979\pi\)
\(830\) 14.4705 32.5013i 0.502278 1.12814i
\(831\) −24.4533 + 42.3543i −0.848275 + 1.46925i
\(832\) 22.5751 16.2729i 0.782651 0.564163i
\(833\) −9.42782 + 6.84971i −0.326655 + 0.237329i
\(834\) −9.23672 43.4554i −0.319842 1.50474i
\(835\) −19.9938 4.24982i −0.691915 0.147071i
\(836\) −0.442014 0.765591i −0.0152874 0.0264785i
\(837\) −1.85107 + 16.6257i −0.0639823 + 0.574667i
\(838\) 19.6275 11.3319i 0.678021 0.391456i
\(839\) 2.04351 + 1.83998i 0.0705497 + 0.0635232i 0.703651 0.710546i \(-0.251552\pi\)
−0.633102 + 0.774069i \(0.718218\pi\)
\(840\) −2.43003 + 2.18801i −0.0838442 + 0.0754936i
\(841\) −11.0751 4.93095i −0.381900 0.170033i
\(842\) 36.9874 1.27467
\(843\) −50.2813 + 29.0299i −1.73178 + 0.999844i
\(844\) 1.70641 + 16.2354i 0.0587371 + 0.558846i
\(845\) 18.6243 41.0016i 0.640697 1.41050i
\(846\) 0.997732 9.49279i 0.0343027 0.326369i
\(847\) −1.05399 + 0.342461i −0.0362154 + 0.0117671i
\(848\) 15.3253 11.1345i 0.526274 0.382360i
\(849\) −0.375268 1.15496i −0.0128792 0.0396380i
\(850\) −2.56698 12.0767i −0.0880468 0.414228i
\(851\) 48.1885 66.3258i 1.65188 2.27362i
\(852\) −3.09961 14.5825i −0.106191 0.499589i
\(853\) 50.0490 + 16.2619i 1.71365 + 0.556797i 0.990934 0.134352i \(-0.0428953\pi\)
0.722712 + 0.691149i \(0.242895\pi\)
\(854\) 0.354893 + 0.257845i 0.0121442 + 0.00882327i
\(855\) 0.937895 2.88654i 0.0320753 0.0987177i
\(856\) 19.5697 + 17.6206i 0.668878 + 0.602261i
\(857\) 19.7605 + 8.79793i 0.675005 + 0.300531i 0.715464 0.698650i \(-0.246215\pi\)
−0.0404592 + 0.999181i \(0.512882\pi\)
\(858\) −12.0241 8.80498i −0.410494 0.300597i
\(859\) −0.463918 + 4.41389i −0.0158287 + 0.150600i −0.999581 0.0289285i \(-0.990790\pi\)
0.983753 + 0.179528i \(0.0574572\pi\)
\(860\) 6.98079 + 15.6791i 0.238043 + 0.534653i
\(861\) 0.356055 + 0.158526i 0.0121343 + 0.00540254i
\(862\) 27.1325 0.924137
\(863\) 47.4297 27.3835i 1.61452 0.932146i 0.626221 0.779646i \(-0.284601\pi\)
0.988303 0.152501i \(-0.0487326\pi\)
\(864\) 5.57469 12.5210i 0.189655 0.425972i
\(865\) −46.5389 15.1214i −1.58237 0.514143i
\(866\) 24.8782 8.08343i 0.845397 0.274686i
\(867\) −15.2389 26.3946i −0.517540 0.896406i
\(868\) −0.613763 0.359417i −0.0208325 0.0121994i
\(869\) −3.76317 2.17267i −0.127657 0.0737028i
\(870\) −9.96193 30.6597i −0.337741 1.03946i
\(871\) 2.55535 0.819716i 0.0865848 0.0277750i
\(872\) −42.9245 + 31.1865i −1.45361 + 1.05611i
\(873\) 1.64319i 0.0556135i
\(874\) −2.11560 3.66433i −0.0715613 0.123948i
\(875\) 0.809791 0.588348i 0.0273759 0.0198898i
\(876\) 0.939614 1.29327i 0.0317466 0.0436954i
\(877\) 1.55413 + 3.49064i 0.0524793 + 0.117870i 0.937882 0.346954i \(-0.112784\pi\)
−0.885403 + 0.464825i \(0.846117\pi\)
\(878\) 6.08959 28.6493i 0.205514 0.966866i
\(879\) −12.2140 + 27.4331i −0.411968 + 0.925295i
\(880\) 2.83184 + 8.71552i 0.0954614 + 0.293800i
\(881\) 17.0931 52.6072i 0.575882 1.77238i −0.0572751 0.998358i \(-0.518241\pi\)
0.633157 0.774023i \(-0.281759\pi\)
\(882\) 11.7234 + 1.23218i 0.394748 + 0.0414897i
\(883\) 13.6973 42.1560i 0.460951 1.41866i −0.403052 0.915177i \(-0.632051\pi\)
0.864004 0.503486i \(-0.167949\pi\)
\(884\) 3.57669 3.94252i 0.120297 0.132601i
\(885\) 64.4257 28.6842i 2.16565 0.964208i
\(886\) −32.2564 10.4807i −1.08368 0.352107i
\(887\) −27.6308 + 30.6871i −0.927752 + 1.03037i 0.0717047 + 0.997426i \(0.477156\pi\)
−0.999457 + 0.0329475i \(0.989511\pi\)
\(888\) 7.65909 + 72.8714i 0.257022 + 2.44540i
\(889\) −0.795155 0.715960i −0.0266686 0.0240125i
\(890\) −18.4298 41.3940i −0.617768 1.38753i
\(891\) −20.3972 2.14383i −0.683332 0.0718211i
\(892\) −14.2050 + 1.49301i −0.475619 + 0.0499895i
\(893\) 3.09654 0.103622
\(894\) −17.2366 −0.576478
\(895\) 83.0292 8.72672i 2.77536 0.291702i
\(896\) 0.0938260 + 0.104204i 0.00313451 + 0.00348122i
\(897\) 45.6043 + 33.3951i 1.52268 + 1.11503i
\(898\) 36.3820 1.21408
\(899\) 18.5872 13.3302i 0.619919 0.444588i
\(900\) 4.94832 8.57074i 0.164944 0.285691i
\(901\) 14.5983 16.2130i 0.486339 0.540134i
\(902\) 1.80180 1.62235i 0.0599935 0.0540184i
\(903\) −0.706151 + 1.58604i −0.0234992 + 0.0527801i
\(904\) 17.4794 + 10.0918i 0.581358 + 0.335647i
\(905\) 26.9207 + 15.5427i 0.894876 + 0.516657i
\(906\) 14.2343 10.3418i 0.472903 0.343584i
\(907\) −19.2965 + 8.59136i −0.640730 + 0.285271i −0.701271 0.712894i \(-0.747384\pi\)
0.0605415 + 0.998166i \(0.480717\pi\)
\(908\) 8.78298 12.0887i 0.291473 0.401179i
\(909\) 2.39674 2.66185i 0.0794949 0.0882880i
\(910\) −1.81063 0.595816i −0.0600218 0.0197511i
\(911\) −35.8052 7.61063i −1.18628 0.252151i −0.427815 0.903866i \(-0.640717\pi\)
−0.758464 + 0.651715i \(0.774050\pi\)
\(912\) 1.62028 + 0.526460i 0.0536527 + 0.0174328i
\(913\) −1.85439 + 17.6434i −0.0613714 + 0.583910i
\(914\) −27.9729 + 5.94583i −0.925262 + 0.196671i
\(915\) −20.3083 6.59857i −0.671372 0.218142i
\(916\) −6.71810 + 9.24667i −0.221972 + 0.305519i
\(917\) −0.585583 + 0.527261i −0.0193376 + 0.0174117i
\(918\) −1.10179 + 5.18353i −0.0363646 + 0.171082i
\(919\) −3.46897 33.0051i −0.114431 1.08874i −0.889523 0.456890i \(-0.848963\pi\)
0.775093 0.631848i \(-0.217703\pi\)
\(920\) −23.8409 73.3749i −0.786012 2.41910i
\(921\) −27.9916 + 38.5271i −0.922354 + 1.26951i
\(922\) 3.77650 + 2.74379i 0.124372 + 0.0903618i
\(923\) 21.1376 18.8895i 0.695752 0.621755i
\(924\) 0.249936 0.432902i 0.00822229 0.0142414i
\(925\) 78.5036i 2.58118i
\(926\) 3.51108 + 33.4057i 0.115381 + 1.09778i
\(927\) −4.79758 + 14.7654i −0.157573 + 0.484961i
\(928\) −17.8232 + 5.79110i −0.585075 + 0.190102i
\(929\) 4.12042 2.37893i 0.135187 0.0780500i −0.430881 0.902409i \(-0.641797\pi\)
0.566068 + 0.824359i \(0.308464\pi\)
\(930\) −42.6800 9.34712i −1.39953 0.306504i
\(931\) 3.82418i 0.125332i
\(932\) −6.69738 + 7.43819i −0.219380 + 0.243646i
\(933\) 7.04835 1.49817i 0.230753 0.0490480i
\(934\) −14.3360 + 1.50677i −0.469088 + 0.0493031i
\(935\) 5.27710 + 9.14020i 0.172580 + 0.298917i
\(936\) −17.4750 + 1.77055i −0.571188 + 0.0578723i
\(937\) 0.613926 + 5.84111i 0.0200561 + 0.190821i 0.999963 0.00863587i \(-0.00274892\pi\)
−0.979907 + 0.199457i \(0.936082\pi\)
\(938\) −0.0462013 0.103770i −0.00150853 0.00338821i
\(939\) 16.8256 + 12.2245i 0.549083 + 0.398932i
\(940\) 16.9310 + 3.59878i 0.552227 + 0.117379i
\(941\) −16.6365 + 37.3662i −0.542334 + 1.21810i 0.409731 + 0.912206i \(0.365623\pi\)
−0.952065 + 0.305896i \(0.901044\pi\)
\(942\) −31.0145 + 10.0772i −1.01051 + 0.328333i
\(943\) −6.83379 + 6.15318i −0.222539 + 0.200375i
\(944\) 5.59804 + 12.5734i 0.182201 + 0.409229i
\(945\) −1.47085 + 0.312638i −0.0478466 + 0.0101701i
\(946\) 7.22674 + 8.02611i 0.234962 + 0.260951i
\(947\) −50.0043 5.25566i −1.62492 0.170786i −0.752176 0.658962i \(-0.770996\pi\)
−0.872745 + 0.488176i \(0.837663\pi\)
\(948\) −4.41696 + 0.938854i −0.143456 + 0.0304926i
\(949\) 3.02180 + 0.329051i 0.0980916 + 0.0106814i
\(950\) −3.70134 1.64794i −0.120087 0.0534663i
\(951\) −29.7205 + 9.65676i −0.963752 + 0.313142i
\(952\) −0.594604 0.432005i −0.0192712 0.0140014i
\(953\) −3.88337 + 36.9478i −0.125795 + 1.19686i 0.731431 + 0.681915i \(0.238853\pi\)
−0.857226 + 0.514941i \(0.827814\pi\)
\(954\) −21.9478 + 2.30681i −0.710587 + 0.0746857i
\(955\) 41.5258i 1.34374i
\(956\) 12.7027 + 7.33391i 0.410835 + 0.237196i
\(957\) 9.44880 + 13.0052i 0.305436 + 0.420397i
\(958\) −6.92385 + 21.3094i −0.223699 + 0.688476i
\(959\) −0.745850 0.158535i −0.0240848 0.00511937i
\(960\) 49.6564 + 28.6691i 1.60265 + 0.925292i
\(961\) −2.86023 30.8678i −0.0922653 0.995734i
\(962\) −34.6493 + 24.9764i −1.11714 + 0.805272i
\(963\) −4.27089 13.1445i −0.137628 0.423574i
\(964\) −3.23710 15.2294i −0.104260 0.490504i
\(965\) −3.31414 31.5319i −0.106686 1.01505i
\(966\) 1.19626 2.07199i 0.0384891 0.0666651i
\(967\) 30.5879 + 17.6599i 0.983639 + 0.567904i 0.903367 0.428869i \(-0.141088\pi\)
0.0802723 + 0.996773i \(0.474421\pi\)
\(968\) 13.7362 + 18.9063i 0.441499 + 0.607671i
\(969\) 1.95135 + 0.205095i 0.0626864 + 0.00658861i
\(970\) −3.73975 0.393063i −0.120076 0.0126205i
\(971\) 6.73842 + 1.43229i 0.216246 + 0.0459645i 0.314761 0.949171i \(-0.398076\pi\)
−0.0985145 + 0.995136i \(0.531409\pi\)
\(972\) −10.7952 + 7.84320i −0.346258 + 0.251571i
\(973\) 2.10565 + 1.89593i 0.0675039 + 0.0607808i
\(974\) 1.24816 0.265304i 0.0399935 0.00850089i
\(975\) 54.1248 + 0.202714i 1.73338 + 0.00649203i
\(976\) 1.28778 3.96339i 0.0412210 0.126865i
\(977\) −23.1079 + 20.8064i −0.739286 + 0.665656i −0.950127 0.311865i \(-0.899046\pi\)
0.210841 + 0.977520i \(0.432380\pi\)
\(978\) 0.200961 1.91202i 0.00642604 0.0611397i
\(979\) 15.1187 + 16.7910i 0.483196 + 0.536644i
\(980\) −4.44444 + 20.9094i −0.141972 + 0.667927i
\(981\) 27.6941 2.91077i 0.884205 0.0929337i
\(982\) 4.08354 19.2116i 0.130311 0.613065i
\(983\) −1.03579 0.108866i −0.0330366 0.00347229i 0.0879957 0.996121i \(-0.471954\pi\)
−0.121032 + 0.992649i \(0.538620\pi\)
\(984\) 0.859095 8.17374i 0.0273869 0.260569i
\(985\) 68.9834 + 30.7134i 2.19800 + 0.978611i
\(986\) 6.27513 3.62295i 0.199841 0.115378i
\(987\) 0.875467 + 1.51635i 0.0278664 + 0.0482661i
\(988\) −0.356788 1.71002i −0.0113509 0.0544031i
\(989\) −27.4092 30.4411i −0.871563 0.967969i
\(990\) 2.21968 10.4428i 0.0705461 0.331893i
\(991\) −15.0183 + 26.0124i −0.477071 + 0.826312i −0.999655 0.0262766i \(-0.991635\pi\)
0.522584 + 0.852588i \(0.324968\pi\)
\(992\) −5.43370 + 24.8109i −0.172520 + 0.787746i
\(993\) 27.3861i 0.869071i
\(994\) −0.891699 0.802889i −0.0282830 0.0254661i
\(995\) −65.0495 21.1359i −2.06221 0.670052i
\(996\) 10.8363 + 14.9149i 0.343361 + 0.472596i
\(997\) −22.1899 + 38.4340i −0.702761 + 1.21722i 0.264732 + 0.964322i \(0.414716\pi\)
−0.967493 + 0.252896i \(0.918617\pi\)
\(998\) 5.36466 + 9.29186i 0.169815 + 0.294129i
\(999\) −13.7050 + 30.7820i −0.433608 + 0.973899i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 403.2.bt.a.82.12 yes 280
13.10 even 6 403.2.bp.a.361.24 yes 280
31.14 even 15 403.2.bp.a.355.24 280
403.231 even 30 inner 403.2.bt.a.231.12 yes 280
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.bp.a.355.24 280 31.14 even 15
403.2.bp.a.361.24 yes 280 13.10 even 6
403.2.bt.a.82.12 yes 280 1.1 even 1 trivial
403.2.bt.a.231.12 yes 280 403.231 even 30 inner